waterproof around floor drain

We live in a 1960’s ranch house on a concrete slab and decided to renovate the laundry room. The laundry tub (thus washer) was draining into a floor drain through a flex-hose stuck through the grate. Pulled out the vinyl tile, found major mold underneath around the drain. Pulled out the rotten drywall next to it (exterior wall), sill-plate was rotten completely. Although I am pretty handy, I had to get fixed by someone since it is a load bearing wall (costly!). We want to prevent any such damage in the future. Both floor and wall will be tiled. I put on Hardie cement-wall around to prepare for tiling, now tackling the drain issue.

The picture shows what is there. The valves are for washer and for an outside faucet, the culprit for all the damage was a bad stem on the valve (somehow it was bent?) which dripped for years. The drain does have a vapor trap (about 1.5 feet down) since I can see standing water in it. The drain works fine. The room has a very slight slope (towards that corner) but I do not think it was meant to be for drainage. At most it is like 1/8” per foot, and even that is quite irregular. But around that area (about 3x3 feet), there is some slope which I can use. So I am thinking of giving more slope away from wall towards the drain (as much I can afford under the tile) with some thinset and use a paint on water proof membrane (such as Redgard from HD, or Watertight from Lowes).

Is this a good idea? Incidentally, I see some kind of plastic membrane (polyethylene sheet?) embedded under the concrete slab (may be at ½” depth) as the red arrow in the picture shows, but it does not look like waterproofing. If I try to waterproof now, how do I tap into existing drain hole, clamping drains are just to large to fit in there. We really do not need to water-proof the entire floor, only enough to alert us if there is a similar leak in the future (even that is questionable since I probably can not slope more than the tile thickness which means I will not see surface water for small drips.) Will waterproof membrane make things worse?

Thanks O'Mike. I guess the better choice is to convert to a "stand pipe" (is that what it is called).

If I can make a water tight seal between the stand pipe and the existing floor drain. Would epoxy work? Or some other material, like some kind of cement?

What is the trick with a stand-pipe? Isn't it a simple Tee with side connecting to the tub drain, the straight up is left open and bottom connecting to the floor drain. I guess the trick would be to have the open end higher than the top of laundry tub so that it can not overflow there. Am I right with these?

Luckily, we are at the "top" of sewer system on our street being the first house. We never have back-ups because of other houses, but back ups because of our connection to the sewer is almost a yearly event because of the huge maple tree in our yard planted right above the main sewer connection of our house. When we notice something, we get the line snaked and everything is Ok. Of course the trick is noticing something in time.

In fact, that is why I want to waterproof around that drain. It is hidden from sight behind the washer. And the slope is towards the wall, so we do not immediately notice any overflow there. Back-up usually shows up in our shower which I think is too late.

Hope these make sense, being an engineer sometimes I tend to over analyze the situation and over design solutions